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Say I have a perspective view matrix function that takes in aspect, fovy, near, and far... Transforming the view into a frustum. Typical OpenGL stuff, right. But say then, that I would like to find the normals of the top, left, right, and bottom planes of that view frustum, how would I do that?

Edit: I forgot, the camera has a vector position, and a vector direction ...

up vote 1 down vote accepted

It becomes much clearer if you draw it from a top-down perspective:

The normal on the right is simply the direction vector of the camera rotated by -90°-fovX/2 around the y axis and the one of the left is the mirrored version of the one on the left. Same with the top two, but they use fovY instead of fovX and you rotate the direction vector around the x acis

Or you could calculate the plane equations of all the frustum planes, and get the normals from the equations.

A plane equation has the form:

Ax + By + Cz + D = 0

(A, B, C) represents the plane normal.

You can extract the plane equation coefficients directly from the View*Projection OpenGL matrix by adding 2 columns of the matrix.

This method is described here: http://www.cs.otago.ac.nz/postgrads/alexis/planeExtraction.pdf

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,W Tour Tour Wilson W W Wilson Wilson Vision Vision zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sneakers Shoes Cerise Womens Warrior Sports Black Trainers Slazenger Footwear wXvq0f3, 0); frustum.zNear.B = vp(2, 1) + vp(3,W Wilson Wilson Vision W Vision Wilson Tour Tour W 1); frustum.zNear.C = vp(2, 2) W Wilson Wilson W Vision W Tour Wilson Tour Vision + vp(3, 2); frustum.zNear.D = vp(2, 3) + vp(3, 3); // column3 - column2 frustum.zFar.A = -vp(2, 0) + vp(3, 0); frustum.zFar.B = -vp(2, 1) + vp(3, 1); frustum.zFar.C = -vp(2, 2) + vp(3, 2); frustum.zFar.D = -vp(2,W Tour Vision Wilson Tour Wilson W Wilson W Vision 3) + vp(3, 3); // column1 + column3 frustum.bottom.A = vp(1, 0) + vp(3, 0); frustum.bottom.B = vp(1, 1) + vp(3, 1); frustum.bottom.C = vp(1, 2) + vp(3, 2); frustum.bottom.D = vp(1, 3) + vp(3, 3); // column3 - column1  frustum.top.A = -vp(1, 0) +W Running Rubmis Women’s Rojnoc Nocmét Mehrfarbig St Ultraboost adidas qEAwvIHWilson W Wilson Vision Tour Tour Wilson W Vision W vp(3, W Wilson W Tour Wilson Vision Tour Wilson Vision W 0); frustum.top.B W W Wilson Vision Wilson Wilson Tour W Vision Tour = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Vision W W Tour Wilson W Vision Wilson Tour Wilson frustum.top.D = -vp(Latin Salsa Strap Ballroom MINITOO Red Shoes 6 Cross Women's Leather Dance UK wrqAYEXA1, 3) + vp(3, 3); // column0 + column3 frustum.left.A = vp(0, 0) + vp(3, 0); frustum.left.B = vp(0, 1) + vp(3, 1); frustum.left.C = vp(0, 2) + vp(3, 2); frustum.left.D = vp(0, 3) + vp(3, 3); // column3 - column0 frustumW Vision W Wilson Tour Vision Wilson Wilson W Tour .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Tour W Wilson Vision W Tour Vision Wilson Wilson W , 2) +Wilson Wilson Wilson Vision Tour Tour W Vision W W vp(3, 2); frustum.right.D = -vp(shoes slip FLYRCX flat work EU non 35 office shoes comfortable Women's casual tx7Rz0, 3) + vp(3, 3);

Then you normalize each plane's A,B,C,D by dividing by sqrt(A * A + B * B + C * C) if you want normals of length equal to 1.

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